Random deposition with a power-law noise model: Multiaffine analysis

2019 ◽  
Vol 99 (1) ◽  
Author(s):  
S. Hosseinabadi ◽  
A. A. Masoudi
Keyword(s):  
Power Law ◽  
Noise Model ◽  
Power Law Noise

scholarly journals Validation of a power-law noise model for simulating small-scale breast tissue

2013 ◽  
Vol 58 (17) ◽  
pp. 6011-6027 ◽  
Author(s):  
I Reiser ◽  
A Edwards ◽  
R M Nishikawa
Keyword(s):  
Power Law ◽  
Breast Tissue ◽  
Noise Model ◽  
Small Scale ◽  
Power Law Noise

Mean amplitudes of the signal in the seasonal and shorter period length of day time series computed by the frequency-dependent autocovariance

2021 ◽  
Author(s):  
Wieslaw Kosek
Keyword(s):  
Time Series ◽  
Power Law ◽  
Amplitude Spectrum ◽  
Noise Model ◽  
Prediction Errors ◽  
Length Of Day ◽  
Frequency Dependent ◽  
Filter Bandwidth ◽  
Power Law Noise ◽  
The Mean

<p>The frequency-dependent autocovariance (FDA) function is defined in this paper as the autocovariance function of a wideband oscillation filtered by the Fourier transform bandpass filter (FTBPF). It was shown that the FDA estimation is a useful algorithm to detect mean amplitudes of oscillations in a very noisy time series. In this paper the least-squares polynomial harmonic model was used to remove the trend, low frequency as well as the annual and semi-annual oscillations from the IERS eopc04R_IAU2000_daily length of day (LOD) time series to compute their residuals. Next, the mean amplitudes of the signal as a function of frequency were determined from the difference between the FDA of LOD residuals and FDA of power-law noise model similar to the noise present in LOD residuals.  Several power-law noise model data were generated with a similar spectral index and variance as the noise in LOD data to estimate the mean amplitude spectrum in the seasonal and shorter period frequency band.  It was shown that the mean amplitudes of the oscillations in LOD residuals are very small compared to the noise standard deviation and do not depend on the filter bandwidth of the FTBPF. These small amplitudes explain why LOD prediction errors increase rapidly with the prediction length.</p>

NONLINEAR TIME SERIES PREDICTION BASED ON A POWER-LAW NOISE MODEL

2007 ◽  
Vol 18 (12) ◽  
pp. 1839-1852 ◽  
Author(s):  
FRANK EMMERT-STREIB ◽  
MATTHIAS DEHMER
Keyword(s):  
Time Series ◽  
Power Law ◽  
Mean Squared Error ◽  
Likelihood Function ◽  
Logistic Map ◽  
Optimization Procedure ◽  
Nonlinear Time Series ◽  
Noise Model ◽  
Annual Number ◽  
Power Law Noise

In this paper we investigate the influence of a power-law noise model, also called Pareto noise, on the performance of a feed-forward neural network used to predict nonlinear time series. We introduce an optimization procedure that optimizes the parameters of the neural networks by maximizing the likelihood function based on the power-law noise model. We show that our optimization procedure minimizes the mean squared error leading to an optimal prediction. Further, we present numerical results applying our method to time series from the logistic map and the annual number of sunspots and demonstrate that a power-law noise model gives better results than a Gaussian noise model.

Breast tissue characterization based on modeling of ultrasonic echoes using the power-law shot noise model

2003 ◽  
Vol 24 (4-5) ◽  
pp. 741-756 ◽  
Author(s):  
M.Alper Kutay ◽  
Athina P Petropulu ◽  
Catherine W Piccoli
Keyword(s):  
Power Law ◽  
Shot Noise ◽  
Breast Tissue ◽  
Tissue Characterization ◽  
Noise Model

scholarly journals SIMULATION OF MAJORITY RULE DISTURBED BY POWER-LAW NOISE ON DIRECTED AND UNDIRECTED BARABÁSI–ALBERT NETWORKS

2008 ◽  
Vol 19 (07) ◽  
pp. 1063-1067 ◽  
Author(s):  
F. W. S. LIMA
Keyword(s):  
Power Law ◽  
Majority Rule ◽  
Noise Spectrum ◽  
Square Lattice ◽  
Complex Environment ◽  
Time Step ◽  
Disorder Phase Transition ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Power Law Noise

On directed and undirected Barabási–Albert networks the Ising model with spin S = 1/2 in the presence of a kind of noise is now studied through Monte Carlo simulations. The noise spectrum P(n) follows a power law, where P(n) is the probability of flipping randomly select n spins at each time step. The noise spectrum P(n) is introduced to mimic the self-organized criticality as a model influence of a complex environment. In this model, different from the square lattice, the order-disorder phase transition of the order parameter is not observed. For directed Barabási–Albert networks the magnetisation tends to zero exponentially and undirected Barabási–Albert networks remain constant.

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